A container of negligible heat capacity contains 1kg of water. It is connected by a steel rod of length 10m and area of cross-section 10cm^(2) to a large steam chamber which is maintained at 100^(@)C. If initial temperature of water is 0^(@)C, find the time after which it beomes 50^(@)C. (Neglect heat capacity of steel rod and assume no loss of heat to surroundings) (use table 3.1, take specific heat of water =4180 J//kg.^(@)C)

A container of negligible heat capacity contains 1kg of water. It is c

1.	A container of negligible heat capacity contains 1kg of water. It is connected by a steel rod of length 10m and area of cross-section 10cm^(2) to a large steam chamber which is maintained at 100^(@)C. If initial temperature of water is 0^(@)C, find the time after which it beomes 50^(@)C. (Neglect heat capacity of steel rod and assume no loss of heat to surroundings) (use table 3.1, take specific heat of water =4180 J//kg.^(@)C)
Answer» Solution :Let temperature of water at TIME t be `T`, then thermal current at time t, `I = ((100 -T)/(R ))` This increases the temperature of water form `T to T +dT` `rArr i = (DH)/(dt) = ms (dT)/(dt)` `rArr (100-T)/(R ) = ms(dT)/(dt) rArr overset(50)underset(0)INT (dT)/(100-T) = overset(t)underset(0)int (dT)/(Rms)` `rArr -ln ((1)/(2)) = (t)/(Rms)` or `t = Rms LN2 sec` `= (L)/(KA) ms ln2 sec` `= ((10m)(1kg)(4180J//kg-^(@)C))/(46(w//m^(@)C)xx(10xx10^(-4)m^(2)))ln2` `= (418)/(46) (0.69) xx 10^(5) = 6.27 xx 10^(5) sec = 174.16 hours`